Course 2024-2025 a.y.

Vector Spaces

Finite-Dimensional Vector Spaces

Linear Maps

Eigenvalues and Eigenvectors

Inner Product Spaces

Operators on Inner Product Spaces

• Explain the basic facts about the relevant topics 

• Describe the theoretical links among mathematical objects 

• Explain in detail some selected topics of Linear Algebra. 

• Illustrate the structure of mathematical reasoning through examples. 

• Use selected basic computational techniques

• Use definitions, theorems and mathematical reasoning to prove simple statements.

• Argue about the correctness of statements using the theorems, definitions and techniques learned in class.

• Practical Exercises
• Individual works / Assignments

• Face to Face lectures present the most important facts about the topics.
• Multiple Exercises sessions help students familiarize with the mathematical reasoning and some simple computational techniques
• Individual assignments offer the students the opportunity to test both their computational skills (through quizzes) and their reasoning skills (through open ended questions).

The exam can be taken in two ways: 

• a single written test (100% of the final grade) 

• some individual written assignments during the semester (50% of the final grade) + an end of semester written test (50% of the final grade) 

All tests and assignments consist of open-ended questions. 

All questions test the student's knowledge and understanding of the basic facts about the relevant topics, their ability to recognize the links among mathematical objects and to use basic computational techniques. Moreover, the questions test the student's ability to use mathematical reasoning to prove simple statements and to argue about the correctness of other statements. 

Linear Algebra Done Right

fourth edition 17 May 2024

© 2024 Sheldon Axler Sheldon Axler

Freely available online